Equivariant operational Chow rings of T-linear schemes

TL;DR

This paper develops a localization theorem for the equivariant Chow cohomology of T-linear schemes, including spherical and Schubert varieties, providing explicit presentations even for singular cases without relying on resolution of singularities.

Contribution

It introduces a resolution-independent localization theorem and explicit descriptions of equivariant Chow cohomology for T-linear schemes, expanding tools for singular spherical varieties.

Findings

Localization theorem for equivariant Chow cohomology of T-linear schemes

Explicit presentation of equivariant Chow cohomology for singular spherical varieties

Applicable to schemes with smooth equivariant envelopes

Abstract

We study $T$-linear schemes, a class of objects that includes spherical and Schubert varieties. We provide a localization theorem for the equivariant Chow cohomology of these schemes that does not depend on resolution of singularities. Furthermore, we give an explicit presentation of the equivariant Chow cohomology of possibly singular complete spherical varieties admitting a smooth equivariant envelope (e.g. group embeddings).